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Verification of Binomial theorem and Chu-Vandermonde convolution by the finite difference method
Chuanan Wei, Dianxuan Gong
In this note, we show that Binomial theorem and Chu-Vandermonde convolution can both be verified by the finite difference method.
Summation formulae for -Watson type -series
Chuanan Wei, Dianxuan Gong, Jianbo Li
According to the method of series rearrangement, we establish two families of summation formulae for -Watson type -series.
Derivative operator and harmonic number identities
Chuanan Wei, Dianxuan Gong
By applying the derivative operator to the corresponding hypergeometric form of a -series transformation due to Andrews [1,Theorem 4], we establish a general harmonic number ide…
A short proof for Dougall's -series identity
Chuanan Wei, Qinglun Yan, Jianbo Li
According to Chen and Fu's method, we offer a short proof for Dougall's -series identity.
-formulas with free parameters
Chuan Wei, Dianxuan Gong, Jianbo Li
In terms of the hypergeometric method, we give the extensions of two known series for . Further, other twenty-nine summation formulas for , and with free paramete…